Dual Bases: Canonical and Dual Spaces

Related lectures (28)

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Explores changing bases in vector spaces and matrix representation of linear transformations.

Covers linear transformations between polynomial spaces and explores examples of linear independence and bases.

Explores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.

Explores linear applications in R² and matrix representation, including basis, operations, and geometric interpretation of transformations.

Explores the relationship between matrices under different bases in linear algebra.

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Emphasizes the importance of using orthogonal bases in linear algebra for representing linear transformations.

Covers kernels and images of linear transformations between vector spaces, illustrating properties and providing proofs.

Explores Lorentz transformations, covariant tensors, rotational invariance, and linear transformations in vector spaces.

Explores subspaces in linear algebra and transformations, including kernels and images of linear transformations.